Barney Stinson has a blog. In it, he posts about his life and the things he likes. He also occasionally posts about his relationships with other characters on the show. Many people believe that Barney does have a blog because the show has included references to it several times.
For example, in one episode, Barney references a blog that he wrote about “How to Flirt With Girls.” It seems likely that this blog is the one that he is referring to. If this is true, then it would appear that Barney does have a blog and that he writes about his life and relationships on it.